Hi kao, welcome to reefs.org.
No Melafix, that stuff is useless. If the fin is eroded/removed down to the caudal peduncle then this is a serious condition. It's either caused by aggression (someone has harrassed this fish, ultimately to death), or disease. No matter the cause, he's in a bad way right now. I would lower the salinity slightly (about 1.015 or so), just to alleviate osmotic stress, and use an actual antibiotic like Spectrogram. Keep his water clean for as long as he lasts, and feed whatever he'll take (freshest is bestest).
Good luck with your little guy!